A random sample of 60 mathematics majors spent an average of $200.00 for textbooks for a term, with a standard deviation of $22.50. A random sample of 40 English majors spent an average of $180.00 for textbooks that term, with a standard deviation of $18.30. Calculate a 90% confidence interval for the difference in average amounts spent on textbooks (math majors - English majors), assuming equal population variances.

Answer:

37

Step-by-step explanation:

(6 × 5) + (10 - 3)

30 + 7

37

Answer:

= 6 items per hour

Explanation:

This is a fraction equal to 18 items ÷ 3 hours

We want a unit rate where 1 is in the denominator, so we divide top and bottom by 3

18 items ÷ 3

3 hours ÷ 3

= 6 items/1 hour

= 6 items/hour

= 6 items per hour

Answer:

a.

Everyone in the Discrete Math class

Everyone in the city

b.

People who receive their pension contribution

Students in a kindergarten class

c.

Twins in the world

Everyone in the world

d.

Miley Cyrus and Dua Lipa

Two blood brothers

Step-by-step explanation:

What we will do is go through each statement and we will give it a true domain and a false domain:

a.) Everyone is studying discrete mathematics.

Domain true = {Everyone in the Discrete Math class}

True because they belong to the math group

Domain false = {Everyone in the city}

False because in the city not everyone gives this type of mathematics.

b.) Everyone is older than 21 years.

Domain true = {People who receive their pension contribution}

True because to receive a pension you have to work for many years.

Domain false = {Students in a kindergarten class}

False because at 21 years old I shouldn't be in kindergarten anymore

c.) Every two people have the same mother.

True domain = {Twins in the world}

True because the twins have the same mother.

Domain false = {Everyone in the world}

False because not everyone has the same mother

d.) No two different people have the same grandmother.

True domain = {Miley Cyrus and Dua Lipa}

True because Miley and Dua don't have the same grandmother

Domain 2 = {Two blood brothers}

False because two blood brothers have the same grandmother

Answer......

x^2+3x+1

Answer:

The answer is x^2+3x+1

Step-by-step explanation:

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

Answer:

10

Step-by-step explanation:

Answer:

10 apples

Step-by-step explanation:

20% of 50 = 10

10 apples

Answer:

its

3 1/2

Step-by-step explanation:

The dilation transformation of the triangle ABC by a scale factor of 3, with the point P as the center of dilation indicates;

Side A'B' will be parallel to side AB

Side A'C' will be parallel to side AC

Side BC will lie on the same line as side BC

A dilation transformation is one in which the dimensions of a geometric figure are changed but the shape of the figure is preserved.

The possible options, from a similar question on the internet are;

Be parallel to

Be perpendicular to
Lie on the same line as

The location of the point P, which is the center of dilation, and the lines PC and PA of dilation and the scale factor of dilation indicates that we get;

PB' = 3 × PB

PA' = 3 × PA

PC' = 3 × PC

Therefore; The side B'C' will be on the same line as the side BC

The Thales theorem, also known as the triangle proportionality theorem indicates that;

The side A'C' will be parallel to the side AC

The side A'B', will be parallel to the side AB

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The correct sequence to model the given scenario is (b) f(n) = 1.12f(n-1)(1- f(n-1/6000)), and we can use this formula to calculate the oxygen released by the tree in each year, option (b) is correct.

The amount of oxygen released by the tree increases at a rate of 12% per year, which is represented by the factor 1.12f(n-1).

However, the tree cannot generate more than 6000 pounds of oxygen per year, which is represented by the limiting factor:

(1- f(n-1/6000)).

To understand this better, let's calculate the oxygen released by the tree in the second year using the formula

f(n) = 1.12f(n-1)(1- f(n-1/6000)).

f(2) = 1.12f(1)(1- f(1)/6000)

= 1.12(250)(1- 250/6000)

= 295.67 pounds of oxygen

Hence, option (b) is correct.

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The correct question is:

Which sequence below would best model the following description? A newly planted tree releases 250 pounds of oxygen over the period of its first year. The amount of oxygen released by the tree grows at a rate of 12% per year, but the tree cannot generate more than 6000 pounds of oxygen per year.

a. f(n) = 1.12f(n-1)(1+ f(n-1/6000)

b. f(n) = 1.12f(n-1)(1- f(n-1/6000)

c. f(n) = 1.12f(n-1) {6000/f(n-1)}

d. f(n) = 1.12f(n-1)(f(n-1) -6000)

Answer:

x=105, y=75 and z=105.....this is a map of parallellines and a transversal. ....angles x and 75 are supplementary angles x=180-75 ×=105...angles y and 75 are corresponding angles so, y=75..angles x and z are alternate exterior angles z=x

Answer:

Step-by-step explanation:

nth term formula

We have

Find a₁₂

Correct choice is B

Answer:

C

Step-by-step explanation:

cot²θ = 1/tan²θ

plug this in to get

1/(1/tan²θ + 1)

1/tan²θ + 1 = 1/tan²θ + tan²θ/tan²θ = (1+tan²θ)/tan²θ

we then have

1/((1+tan²θ)/tan²θ)

1/(x/y) = y/x, so this is equal to

tan²θ/(1+tan²θ)

tan²θ = sin²θ/cos²θ, so plug this in to get

(sin²θ/cos²θ)/(1+sin²θ/cos²θ)

1+sin²θ/cos²θ = cos²θ/cos²θ + sin²θ/cos²θ

sin²θ + cos²θ = 1, so we have

(cos²θ+sin²θ)/cos²θ = 1/cos²θ. plug this in to get

(sin²θ/cos²θ)/(1/cos²θ)

(a/b)/(c/d) = (d/c) * (a/b), so we have

(sin²θ/cos²θ)/(1/cos²θ)  = cos²θ/1 * sin²θ/cos²θ = sin²θ

To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Answer:

x=-4 x=2

Step-by-step explanation:

Divide both sides by 3

(x+1)^2=9

Take the square root of both sides

x+1=-3

x+1=3

Solve for X

x=-4

x=2

x=-4 x=2

Answer:

Step-by-step explanation:

16>-2x

-2x<16

x>-8

3X + 6

I hope this help

Answer:

31.01

Step-by-step explanation:

A= πr^2= π · 3.142 ≈31.01432

Step-by-step explanation:

135.5

+ 27.6

______

163.1

Check the picture below.

so the base of that triangle is AB whilst the height of it is CD, so let's get them

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~2 - (-4)~~)^2 + (~~-8 - (-6)~~)^2} \implies AB=\sqrt{(2 +4)^2 + (-8 +6)^2} \\\\\\ AB=\sqrt{( 6 )^2 + ( -2 )^2} \implies AB=\sqrt{ 36 + 4 } \implies AB=\sqrt{ 40 }\implies \stackrel{base}{AB=2\sqrt{10}} \\\\[-0.35em] ~\dotfill\)

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CD=\sqrt{(~~-7 - (-6)~~)^2 + (~~-5 - (-2)~~)^2} \\\\\\ CD=\sqrt{(-7 +6)^2 + (-5 +2)^2} \\\\\\ CD=\sqrt{( -1 )^2 + ( -3 )^2} \implies CD=\sqrt{ 1 + 9 } \implies \stackrel{height}{CD=\sqrt{ 10 }} \\\\[-0.35em] ~\dotfill\)

\(A=\cfrac{1}{2}(\stackrel{b}{2\sqrt{10}})(\stackrel{h}{\sqrt{10}})\implies A=\sqrt{10}\cdot \sqrt{10}\implies A=\sqrt{10^2}\implies {\Large \begin{array}{llll} A=10 \end{array}}\)

Answer: 81

Step-by-step explanation: 27 times 3 = 81

Answer: 81

Step-by-step explanation: 21 times 3

Both g(x) = 5 - x² and h(x) = \(5 - e^(6-^x^)\)have the same range as f(x) = -2√(x) - 3 + 8, which is (-∞, 5].

To determine which function has the same range as f(x) = -2√(x) - 3 + 8, we need to first find the range of f(x).

The square root function √(x) takes non-negative values as input and gives non-negative outputs, so the expression -2√(x) will always be non-positive. Therefore, the range of f(x) will be all real numbers less than or equal to -3 + 8, which is 5.

In other words, the range of f(x) is (-∞, 5].

So, we need to find a function whose range is also (-∞, 5]. One possible function is g(x) = 5 - x². We can see that when x is zero, g(x) is at its maximum value of 5, and as we increase or decrease x, g(x) will decrease, eventually approaching negative infinity.

Another possible function is h(x) = 5 - e^(-x). When x is negative infinity, e^(-x) is approaching positive infinity, so h(x) is approaching 0. As we increase x, e^(-x) is approaching zero, so h(x) is approaching 5.

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Answer:

\(y=-x+1\)

Step-by-step explanation:

It helps to write the equation in slope-intercept formula to find the slope of an equation in the form: \(y=mx+b\) where "m" is the slope of the equation. We can take the equation given: \(-7x-7y=7\) and solve for "y" to get the equation in slope-intercept form:

\(-7x-7y=7\)

add 7x to both sides:

\(-7y=7x+7\)

Divide both sides by -7

\(y=-x-1\)

Now in this form we can tell that the coefficient of "x" (the m value) is our slope, which is -1. We need this slope to determine a parallel line as parallel lines share the same slope but different y-intercepts. So a general equation for a parallel line would be:

\(y=-x+b\text{ where b }\ne -1\)

We're given the point (-1, 2) and we can use it to solve for that "b" value.

We plug in -1 as x and 2 as y

\(2=-1(-1)+b\implies 2=1+b\implies 1=b\)

Now we just plug this into the general equation to get: \(y=-x+1\)

Answer:

two

Step-by-step explanation:

Answer:

Because we want to know how many three-fourths there are, we have to make groups of 3 fourths, or divide the number of fourths we have by 3. So there are (2\times 4)\div 3 = 8\div 3 = 2 \frac23 three-fourths in 2.

Step-by-step explanation:

Answer:

df=23, T∼t23

Step-by-step explanation:

The degrees of freedom would be calculated as df = n-1 = 24-1 = 23, and the distribution notation would be T∼t23 from the degrees of freedom.

Answer:

Winston can find $1.125 dollars every 1 hour.

Step-by-step explanation:

I got this by dividing 3.75 by 3 1/3.

3.75 ÷ 3 1/3 = 1.125

Hope this helps! :)

Answer:

Just do

Step-by-step explanation:

The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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Answer:

x = 9

Step-by-step explanation:

6/(x - 1) = 21/(3x + 1)

21(x - 1) = 6(3x + 1)

21x - 21 = 18x + 6

3x = 27

x = 9

Answer:

Step-by-step explanation:

To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

This helped me when i was learning to solve for x